The topics of this thesis are the modal μ-calculus and parity games. The modal μ-calculus is a common logic for model-checking in computer science. The modelchecking problem of the modal μ-calculus is polynomial time equivalent to solving parity games, a 2-player game on labeled directed graphs. We present the first FPT algorithms (fixed-parameter tractable) for the model-checking problem of th...

Power consumption is one of the important issues in VLSI design. Reversible logic produces zero power; therefore, nowadays researchers attend to it in order to optimize power. In the digital systems, one of the methods of achieving to fault tolerance is parity preserving. This paper proposes a new parity preserving reversible gate, PPRG. The most significant aspect of the PPRG gate is that it c...

the aim of this study was to investigate the effect of milking frequency (three times daily vs. two times daily) on the lactation curve shape, partial and 305-d lactation performance in holstein dairy cows in iran. data from february 2000 to december 2012 comprising 217345 lactations on 141364 cows distributed in 324 herds collected by the animal breeding center of iran were used. the mean milk...

A Parity Alternating Permutation of the set $[n] = \{1, 2,\ldots, n\}$ is a permutation with even and odd entries alternatively. We deal parity alternating permutations having an entry in first position, PAPs. study numbers that count PAPs as well parity. also subclass being derangements well, Derangements (PADs). Moreover, by considering these PADs we look into their statistical property exced...

The objectives of this study were to characterize sows having high lifetime efficiency and high longevity (HE–HL), to examine the relationship between lifetime measurements, and to determine the association between the sows and herd productivity. This study was conducted by obtaining sow data with 66,262 parity records of 13,786 sows born during 1999 and herd data with mean measurements of 4-ye...

The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are ...

We investigate well-structured graph-driven parity-FBDDs, which strictly generalize the two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Boolean functions represented by wellstructured graph-driven parity-FBDDs in terms of invariants of the function represented and the graph-ordering used. As a consequenc...